1 files changed, 34 insertions, 0 deletions
diff --git a/tutorials/module_3/finiteDifference.py b/tutorials/module_3/finiteDifference.py
new file mode 100644
index 0000000..10470f1
--- /dev/null
+++ b/tutorials/module_3/finiteDifference.py
@@ -0,0 +1,34 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed May  7 10:25:47 2025
+
+@author: christian
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Initiate vectors
+t = np.linspace(0, 30, 5)  # simulate for 20 seconds
+v = 42.78 * (1 - np.exp(-9.81 * t / 42.78))
+
+# Forward difference method
+dvdt_fd = (v[1:] - v[:-1]) / (t[1:] - t[:-1])
+dvdt_bd = (v[1:] - v[:-1]) / (t[1:] - t[:-1])
+dvdt_cd = (v[2:] - v[:-2]) / (t[2:] - t[:-2])
+
+# Plotting
+plt.figure(figsize=(8, 5))
+plt.plot(t, v, label='Velocity (m/s)', color='blue')
+plt.plot(t[:-1], dvdt_fd, label=r'forward difference')
+plt.plot(t[1:], dvdt_bd, label=r'backward difference')
+plt.plot(t[1:-1], dvdt_cd, label=r'central difference')
+plt.axhline(y=42.78, color='red', linestyle='--', label=f'Terminal velocity ≈ {42.78:.2f} m/s')
+plt.title('Falling Object Approaching Terminal Velocity')
+plt.xlabel('Time (s)')
+plt.ylabel('Velocity (m/s)')
+plt.grid(True)
+plt.legend()
+plt.tight_layout()
+plt.show()
+\ No newline at end of file